Cook was born in 1937 in Torquay, Devon. He was educated at Radley College, and came up to Pembroke in 1957 to study French and German, with the intention of becoming a diplomat like his father. While at university, he joined the Cambridge University Liberal Club.

At Pembroke, Cook began to take part in theatre, touring Germany with the Pembroke Players in 1958 in a production of The Merchant of Venice. He wrote and starred in several revues with the Players, as well as with the Cambridge Footlights, of which he was President in 1960. His performances in the latter gathered him attention outside of university and he was recruited to write the major part of the West End revue 'Pieces of Eight' before he had completed his degree.

Throughout Cook’s career, he opened several theatres and continued to write and perform in many comedy and satire shows. He also success on film and television, particularly in partnership with Dudley Moore. Cook died in London in 1995. The Peter Cook Fund has since been established at Pembroke, providing funding for selected students each year to travel and tour with a theatre production.